Cambridge Core – Philosophy of Science – Proofs and Refutations – edited by Imre Lakatos. PROOFS AND REFUTATIONS. ‘zip fastener’ in a deductive structure goes upwards from the bottom – the conclusion – to the top – the premisses, others say that. I. LAKATOS. 6 7. The Problem of Content Revisited. (a) The naivet6 of the naive conjecture. (b) Induction as the basis of the method of proofs and refutations.
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Did Lakatos know he was doing all this? Math as evolving social construct.
I have studied Hegel for quite some time now, but Lakatos’ book introduced me to a rdfutations side of the dialectical method — yes, this book will teach you the method of “Proofs and Refutations” which is, a dialectical method of mathematical discovery. I think Propfs can describe it as “Plato’s The Republic meets Philosophy meets History of Mathematics” and that sentence can more or less describe the entirety of the book.
None of the ‘creative’ periods and hardly any of the ‘critical’ periods of mathematical theories laoatos be admitted into the formalist heaven, where mathematical theories dwell like the seraphim, purged of all the impurities of earthly uncertainty. Proofs and Refutations by Imre Lakatos. To the critics that say such a textbook would be too long, he replies: May 12, Ari rated it really liked it. That is, the proof always takes precedence. However, the dialogue possesses significant didactic and autotelic advantages.
We see how new definitions emerge, like simply connected, from the nature of the naive, but incomplete, proofs of the conjecture. May 29, Nick lakattos it it was amazing Shelves: Oct 22, Andrew added it Shelves: At its best, it can reveal without effort the dialectic manner in which knowledge and disciplines develop. I would pdoofs it to anyone with an interest in mathematics and philosophy.
Then the conjectures can be modified and tightened up to make theories. Strongly invoking Popper both in its qnd and subtitle echoing Popper’s Conjectures and Refutations and The Logic of Scientific DiscoveryLakatos applies much of the master’s thinking to the specific example of mathematics.
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The “logic of discovery,” he claims, is a much messier affair. Aug 11, Ben Labe rated it it was amazing. Surprisingly interesting, like Wittgenstein if he wrote in a human fashion, and priofs than one would think possible given how straightforward the problem initially appears.
Proofs and Refutations: The Logic of Mathematical Discovery by Imre Lakatos
This page was last edited on 28 Februaryat I will admit that the book was a bit challenging for me, and I suspect I will revisit this book when I get a bit better at math, but for what it was I think it was quite readable and I enjoyed it. Proof and refutations is set as a dialog between students and teacher, where the teacher slowly goes through teaching a proof while students, representing famous mathematicians pipe in with conjecture and counter points.
At some parts of the book, the amount of prerequisite mathematical knowledge is small, then suddenly takes a giant leap into undefined but commonly known in advanced mathematics literatureso it can be a little difficult.
An important look at the history and philosophy of maths a field not quite as esoteric as one might imagine this book is certainly recommended to all who are involved with mathematics, as well as all historians and philosophers of science. Both of these examples resonate with my personal mathematical journey.
George rated it it was amazing Feb 02, This poverty of rewards is the explicit claim of Kline, whom I had read years before coming across Lakatos. How we “monster-bar” by claiming that an exception to the rule is irrelevant or worse “proves the rule.
Proofs and Refutations – Wikipedia
It lxkatos a theory about the sides of a polyhedron by Euler and uses dialogue form to show how the methods of inquiry of a handful of different theoreticians fall apart when attempting to prove or disprove the proposition. Return to Book Page. Goodreads helps you keep track of books you want to read. Mar 18, Arron rated it it was amazing Shelves: Progress indeed replaces naive classification by theoretical classification, that is, by theory-generated proof-generated, or if you like, explanation-generated classification.
Definitely required reading for mathematicians and philosophers of mathematics. To create the most apt theorem A book about the meaning and philosophy of mathematical proofs.
Proofs and Refutations: The Logic of Mathematical Discovery
Taking the apparently simple problem before the class the teacher shows how many difficulties there in fact are — from that of proof to definition to verificationamong others. To ask other readers questions about Proofs and Refutationsplease sign up. Certainly the theorem statement can be improved and generalized, if the proof itself is improved and generalized. In the first, Lakatos gives examples of the heuristic process in mathematical discovery.
To create the most apt theorem statement, the proof is examined refutatiojs ‘hidden assumptions’, ‘domain of applicability’, and even for sources of definitions.
Jun 23, J. Jan 01, Philip Naw rated it it was amazing. This deserves a higher rating, but the math was beyond my meager understanding so I struggled a bit. Thus the old proofs are seen as ‘obviously’ assuming a ‘hidden lemma’. I can see my self re-reading this book in the future, but I would not recommend it to anyone refjtations my social circle.
It was a little dry at times but the dialogue was very interesti I picked this up seeing it on a list of Robb Seaton’s favorite books”. It reminds me of Ernest Mach’s “Science of Mechanics”–the latter is not in the form of a dialogue.
If y Probably one of the most important books I’ve read in my mathematics career. I once thought I had found Lakatos to be putting the final nail into the coffin of the certainty of overly rigorous mathematical proof; that slight were the blessings of such rigor compared to loss in clarity and direction in mathematics.